On the representation of local indistinguishability operators

Calvo, Tomasa; Recasens, J.

doi:10.1016/j.fss.2020.06.009

Cited by 7 publications

(4 citation statements)

References 14 publications

(26 reference statements)

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“…The previous results were generalized in (Valverde 1985) to general continuous tnorms, though all results and proofs remain valid for complete residuated lattices and in particular for left-continuous t-norms. (Fodor and Roubens 1995) proved a representation theorem for transitive fuzzy relations and in (Calvo and Recasens 2021) a representation theorem for local fuzzy equivalence relations (i.e., non-necessarily reflexive) can also be found.…”

Section: The Representation Theoremmentioning

confidence: 95%

“…• t-norms are decomposable local (i.e. : non-reflexive) fuzzy equivalence relations (Calvo and Recasens 2021).…”

Section: Decomposable Fuzzy Equivalence Relationsmentioning

confidence: 99%

“…To finish this subsection, let us point out that for local fuzzy equivalence relations (i.e. : non-necessarily reflexive) extensionality must be referred to couples of fuzzy subsets (Calvo and Recasens 2021).…”

Section: The Set H E Of Extensional Fuzzy Subsetsmentioning

confidence: 99%

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Fifty years of similarity relations: a survey of foundations and applications

Recasens

2021

International Journal of General Systems

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Section: The Representation Theoremmentioning

confidence: 95%

“…• t-norms are decomposable local (i.e. : non-reflexive) fuzzy equivalence relations (Calvo and Recasens 2021).…”

Section: Decomposable Fuzzy Equivalence Relationsmentioning

confidence: 99%

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Fifty years of similarity relations: a survey of foundations and applications

Recasens

2021

International Journal of General Systems

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“…Since indistinguishability fuzzy relations were introduced by Trillas, many authors have explored their properties, methods for generating them, and their applications (see, for instance, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Aggregation of Indistinguishability Fuzzy Relations Revisited

2021

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Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

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